Copula modeling for the estimation of measures of marker classification and predictiveness performance with survival outcomes.

The discriminative and predictive power of a continuous-valued marker for survival outcomes can be summarized using the receiver operating characteristic and predictiveness curves, respectively. In this paper, fully parametric and semi-parametric copula-based constructions of the joint model of the marker and the survival time are developed for characterizing, plotting, and analyzing both curves along with other underlying performance measures. The formulations require a copula function, a parametric specification for the margin of the marker, and either a parametric distribution or a non-parametric estimator for the margin of the time to event, to respectively characterize the fully parametric and semi-parametric joint models. Estimation is carried out using maximum likelihood and a two-stage procedure for the parametric and semi-parametric models, respectively. Resampling-based methods are used for computing standard errors and confidence bounds for the various parameters, curves, and associated measures. Graphical inspection of residuals from each conditional distribution is employed as a guide for choosing a copula from a set of candidates. The performance of the estimators of various classification and predictiveness measures is assessed in simulation studies, assuming different copula and censoring scenarios. The methods are illustrated with the analysis of two markers using the familiar primary biliary cirrhosis data set.

A multi-source global-local model for epidemic management.

The Effective Reproduction Number Rt provides essential information for the management of an epidemic/pandemic. Projecting Rt into the future could further assist in the management process. This article proposes a methodology based on exposure scenarios to perform such a procedure. The method utilizes a compartmental model and its adequate parametrization; a way to determine suitable parameters for this model in México's case is detailed. In conjunction with the compartmental model, the projection of Rt permits estimating unobserved variables, such as the size of the asymptomatic population, and projecting into the future other relevant variables, like the active hospitalizations, using scenarios. The uses of the proposed methodologies are exemplified by analyzing the pandemic in a Mexican state; the main quantities derived from the compartmental model, such as the active and total cases, are included in the analysis. This article also presents a national summary based on the methodologies to illustrate how these procedures could be further exploited. The supporting information includes an application of the proposed methods to a metropolitan area to show that it also works well at other demographic disaggregation levels. The procedures developed in this article shed light on how to develop an effective surveillance system when information is incomplete and can be applied in cases other than México's.

A flexible special case of the CSN for spatial modeling and prediction.

We introduce a parsimonious, flexible subclass of the closed-skew normal (CSN) distribution that produces valid stationary spatial models. We derive and prove some relevant properties for this subfamily; in particular, we show that it is identifiable, closed under marginalization and conditioning and that a null correlation implies independence. Based on the subclass, we propose a discrete spatial model and its continuous version. We discuss why these random fields constitute valid models, and additionally, we discuss least-squares estimators for the models under the subclass. We propose to perform predictions on the model using the profile predictive likelihood; we discuss how to construct prediction regions and intervals. To compare the model against its Gaussian counterpart and show that the numerical likelihood estimators are well-behaved, we present a simulation study. Finally, we use the model to study a heuristic COVID-19 mortality risk index; we evaluate the model's performance through 10-fold cross-validation. The risk index model is compared with a baseline Gaussian model.